A windmill captures 700W of wind power for 17h. The kinetic energy is converted to electric energy and stored in a battery, before being used by a 20W light bulb. During the process 68% of the energy is lost.

wind energy captured: ___W h
loss: ___W h
energy delivered to light bulb: ___W h

How long could the light bulb be used? ____hours

Answer: [tex]1.67\ V[/tex]

Explanation:

Given

Work function [tex]\phi =1.17\ eV[/tex]

The wavelength of the light is [tex]\lambda =437\ nm[/tex]

Energy associated with this wavelength is

[tex]E=\dfrac{hc}{\lambda}\\\\\Rightarrow E=\dfrac{1.99\times 10^{-25}}{437\times 10^{-9}}\\\\\Rightarrow E=4.553\times 10^{-19}\ J\\\\\Rightarrow E=2.841\ eV[/tex]

Stopping potential is

[tex]V=\dfrac{E-\phi }{e}\\\\\Rightarrow V=\dfrac{\left(2.841-1.17\right)e}{e}\\\\\Rightarrow V=1.67\ V[/tex]

Answer:

Solution given:

Radius of small sphere[r]=5cm=0.05m

Radius of large sphere[R]=10cm=0.1m

capacitance of small sphere[c]=4πε0r

=[tex]4π*8.85×10^{-12}×0.05=5.56*10^{-12}F[/tex]

Charge for small sphere[Q1]=100C

Charge for small sphere[Q2]=50C

Potential difference [V1]=[tex] \frac{charge}{capacitance}=\frac{100}{5.56*10^{-12}}=1.8×10^{13}[/tex]V

.

again

capacitance of small sphere[C]=4πε0R

=[tex]4π*8.85×10^{-12}×0.1=1.11*10^{-11}F[/tex]

Potential difference [V2]=[tex] \frac{charge}{capacitance}=\frac{50}{1.11*10^{-11}}=4.5×10^{12}[/tex]V

Now

Loss of energy:

[tex] \frac{cC(V1-V2)^{2}}{2(c+C)}[/tex]

=[tex] \frac{5.56*10^{-12}*1.11*10^{-11}(1.8*10^{13}-4.5*10^{12})^{2}}{2(5.56*10^{-12}+1.11*10^{-11})}[/tex]

=25Joule

Answer:

Un'auto si muove lungo un percorso rettilineo con velocità variabile come mostrato in figura. Quando l'auto è in possesso di A, la sua velocità è 10 ms-1 e quando è in posizione B, la sua velocità è 20 ms-1. Se l'auto impiega 5 secondi per spostarsi da A a B, trova l'accelerazione dell'auto.

Explanation:

Answer: 708 N

Explanation:

Given

At rest, Elevator reads 588 N

When it starts moving upward at [tex]2\ m/s^2[/tex], apparent weight changes

i.e. weight can be given by

[tex]\Rightarrow W'=m(g+a)\\\Rightarrow W'=mg+mg\cdot \dfrac{a}{g}\\\\\Rightarrow W'=W\left(1+\dfrac{a}{g}\right)\\\\\Rightarrow W'=588\left(1+\dfrac{2}{9.8}\right)\\\\\Rightarrow W'=707.99\approx 708\ N[/tex]

The apparent weight is 708 N

A tennis ball and a bowling ball can have the same momentum. This is because, it depends upon both the mass of object and velocity of object.

Momentum can be defined as the mass in motion. All objects which have mass so, if an object is moving in space, then it has some amount of momentum which has its mass in motion. The amount of momentum which an object has depend upon two variables which include how much stuff is moving that is the mass of object and how fast the stuff is moving that is the speed.

A fast-moving tennis ball may have the same momentum as a slow-bowling ball. It is important to understand here that the momentum of an object which depends on the product of the mass and velocity of an object, but not the mass or the velocity alone.

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Answer:

the magnitude of the average contact force exerted on the leg is  3466.98 N

Explanation:

Given the data in the question;

Initial velocity of hand v₀ = 5.25 m/s

final velocity of hand v = 0 m/s

time interval t = 2.65 ms = 0.00265 s

mass of hand m = 1.75 kg

We calculate force on the hand F[tex]_{hand[/tex]

using equation for impulse in momentum

F[tex]_{hand[/tex] × t = m( v - v₀ )

we substitute

F[tex]_{hand[/tex] × 0.00265  = 1.75( 0 - 5.25 )

F[tex]_{hand[/tex] × 0.00265  = 1.75( - 5.25 )

F[tex]_{hand[/tex] × 0.00265  = -9.1875

F[tex]_{hand[/tex] = -9.1875 / 0.00265  

F[tex]_{hand[/tex] = -3466.98 N

Next we determine force on the leg F[tex]_{leg[/tex]

Using Newton's third law of motion

for every action, there is an equal opposite reaction;

so, F[tex]_{leg[/tex] = - F[tex]_{hand[/tex]

we substitute

F[tex]_{leg[/tex] = - ( -3466.98 N )

F[tex]_{leg[/tex] = 3466.98 N

Therefore, the magnitude of the average contact force exerted on the leg is  3466.98 N

Answer:

B. Frequency

Explanation:

Answer:

Magnitude of the average force = 7.85 N

Explanation:

Data given:

Mass of bullets, m = 6.4 g

Rate of bullets/min, r = 92 bullets/min

Speed of each bullet, v = 400 m/s

Change in momentum here, Δ B = Bf - Bi

where f is the final and i is the initial

Note that change in momentum = force X time

So, Δ B = m(vf - vi)

              = 2mv

             = 2 X 0.0064 kg X 400 m/s        (convert g to kg)

            = 5.12 kg.m/s (for one bullet)

        so for the 92 bullets = 92 X 5.12 kg.m/s

           = 471.04 kg.m/s

         The force = Δ B ÷ Δt

where t = time measured in 60 seconds

        =  471.04 kg.m/s ÷ 60 seconds

       = 7.85 N

Answer:

The total resistance is 106 Ω and the current in the circuit is 0.11 A.

Explanation:

Given that,

Voltage of the battery, V = 12 V

Resistors 34 Ω, 42Ω, and 30Ω are connected in series.

The total resistance is given by :}

R = 34 + 42 +30

= 106Ω

Let I is the total current in the circuit. Using ohm's law to find it such that,

[tex]I=\dfrac{V}{R}\\\\I=\dfrac{12}{106}\\\\I=0.11\ A[/tex]

Hence, the total resistance is 106 Ω and the current in the circuit is 0.11 A.

Answer and Explanation:

The answer is the second answer choice. This is because we humans can rebuild or build memories during the day, it doesn't have to happen via sleep.

The first answer choice IS a reason because you aren't working your brain as hard, so your brain has time to heal. A mouse study suggests that sleep helps restore the brain by flushing out toxins that build up during waking hours.

The third answer choice IS a reason because of the idea of Wish Fulfillment: Sigmund Freud suggested that dreams provide a psychic safety valve to discharge unacceptable feelings. The dream's manifest (apparent) content may also have symbolic meanings (latent content) that signify our unacceptable feelings.

The forth answer choice IS a reason because of the idea of Cognitive Development: Some researchers argue that we dream as a part of brain maturation and cognitive development.

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Answer:

[tex]I=0.0987kg.m^2[/tex]

Explanation:

From the question we are told that:

Mass [tex]M=1.80kg[/tex]

Deviation [tex]d=0.250[/tex]

Time [tex]t=0.940s[/tex]

Generally the equation for moment of inertia is mathematically given by

 [tex]I=\frac{T}{2\pi}^2(mgd)[/tex]

 [tex]I=\frac{0.94}{2.3.142}^2(1.80*9.8*0.250)[/tex]

 [tex]I=0.0987kgm^2[/tex]

Answer:

19

Explanation:

I legit did this and it took 19.

Answer:

P = 756.84 Watts

Explanation:

As the tension is stationary or innitial, T₀ = 31 N, the mean would be:

T₁ + T₂ / 2 = T₀    (1)

T₁ + T₂ = 2 * 31 = 62 N

Now, with the following expression we can determine the linear speed:

V = πWD  (2)

W: angular speed of the wheel  (rev/s)

D: diameter of the wheel (in meters)

W = 1547 rev/min * (1 min/60 s) = 25.78 rev/s

V = π * 25.78 * 0.379 = 30.695 m/s

We also know that:

T₁ / T₂ = exp (μθ)

T₁ = T₂ exp(μθ)   (3)

We already have those values so replacing:

T₁ = T₂ exp(0.3 * 161 * π/180)

T₁ = 2.32T₂   (4)

We can now replace (4) in (1) like this:

T₁ + T₂ = 62 N

2.32T₂ + T₂ = 62

3.32T₂ = 62

T₂ = 18.67 N

Which means that T₁:

T₁ = 2.32(18.67)

T₁ = 43.33 N

Finally, the power can be determined using the following expression:

P = (T₁ - T₂)V  (5)       Replacing we have:

P = (43.33 - 18.67)*30.695

Hope this helps

Answer:

The correct answer is -

B. The velocity would double (v = 2v).

C. The wavelength would be half (λ = λ/2).

Explanation:

A wave has a speed or velocity that is related to the wavelength of the wave and the frequency of the wave and this relationship can be represented by the following equation-

Wave velocity V = Wavelength (λ) * Frequency (f)

Frequency (f) = Velocity (V) / Wavelength(λ).

The frequency and wavelength are inversely proportional and frequency and velocity are directly proportional to each other.

So, if f = 2f then,

putting value in the formula,

2f = 2v/λ, which means, f = 2v and f = λ/2

when the frequency is doubled, the wavelength will be halved and velocity will be doubled.

Answer:

9.2 V

Explanation:

The RMS value of an AC is the effective value of a varying voltage or current in DC, that is the equivalent value of the AC which produces the same effect as an DC. For example if a motor is supplied by a 9V RMS voltage, it will rotate as if the voltage applied was 9V DC.

The RMS value is given by:

RMS voltage = Peak voltage * 1/√2

Given that the maximum voltage should not exceed 13 V, this means that the peak voltage is 13 V. The maximum RMS voltage is:

RMS voltage = Peak voltage * 1/√2 = 13 * 1/√2 = 9.2 V

F = Kq₁q₂/(r)²

K is a constant

R is the distance between them

F = 9.0 E9 × 1.0 E-6 × 1.0 E-6/(0.30)²

= 9.0E-3/0.30² = 9.0E-3/0.09 = 0.1 N

The electrostatic force of repulsion between two charges can be determined using Coulomb's law of electrostatic force. The force of repulsion between the point charges of magnitude 1 ×10 ⁻⁶ C separated by 0.30 m is 0.1 N.

According Coulomb's law of electrostatic forces, the force between two charges q1 and q2 separated by a distance of r meters is given by the expression:

F =  K q1 q2/r²

Where, K is Coulomb's Constant equal to  9.0 ×10⁹ Nm²/C²

Given q1 = q2 = 1 ×10 ⁻⁶ C

r = 0.30 m

k = 9.0 ×10⁹ Nm²/C².

Then the electrostatic force of repulsion between the two point charges is calculated as follows:

F = 9.0 ×10⁹ Nm²/C² × 1 ×10 ⁻⁶ C × 1 ×10 ⁻⁶ C/ (0.30 m )²

  = 0.1 N.

Therefore, the repulsive force exerted on two point charges that each carry 1.0 E-6 C of negative charge and are 0.30 meters apart is 0.1 N.

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Answer:

I think concave

Explanation:

Answer:

1700 kg

Explanation:

Let’s use conservation of momentum

32.5 * 388 = 7.42 * mc

mc = 1699.46

mc = 1700 kg

Answer:

Gy = 3.14x10⁻⁴ Gy

Explanation:

To get the dose in Gy we need to use the following expression:

Gy = E / m  (1)

Where:

Gy: dose

E: energy absorbed per atom

m: mass of the human body.

We don't have the energy per atom, but we can calculate that by following the next procedure.

First, let's determine the number of atoms of potassium in our body. For that we need to determine the moles in the 140 g of potassium, with the molecular mass and then, use the avogadro's number:

moles = m/MM

moles = 140 / 39.1 = 3.58 moles

N° atoms = 3.58 * 6.02x10²³ atoms = 2.16x10²⁴ atoms of K.

The abundance of the ⁴⁰K is 0.012% so the atoms of this isotope would be:

N = 2.16x10²⁴ * (0.012/100) = 2.59x10²⁰ atoms of ⁴⁰K.

With this number, and the half life rate, we can determine the number of decay atoms in a year (λ) using the following expression:

λ = ln2 / t(1/2)

λ = ln2 / 1.3x10⁹ = 5.33x10⁻¹⁰ year⁻¹

This number, multiplied by the number of atoms:

R = 5.33x10⁻¹⁰ * 2.59x10²⁰ = 1.38x10¹¹ atoms/year

Now, each atom of K gives an average energy of 1 MeV, so with the atoms we have:

E = 1.38x10¹¹ * 1x10⁶ eV = 1.38x10¹⁷ eV

This value can be expressed in Joules so:

E = 1.38x10¹⁷ eV * (1 J / 6.24x10¹⁸ eV) = 0.022 J

Finally, we can use (1) to get the dose in Gy:

Gy = 0.022 / 70

Hope this helps

Answer:

convex       f = 33 cm

concave     f = -33 cm

Explanation:

In geometric optics the focal length of a lens is given by

         [tex]\frac{1}{f} = ( n-1) \ (\frac{1}{R_2} - \frac{1}{R_1} )[/tex]

where n is the refractive index of the medium, R₁ and R₂   are the focal lengths on each side of the lens.

In this case one of the sides is flat so its focal length is infinite, if the lens is convex the focal length is positive, convergent lens and if it is concave the focal length is negative, divergent lens.

         [tex]\frac{1}{f} = (n-1) \ \frac{1}{R}[/tex]

the refractive index of the glass is n = 1.5

let's calculate

         1 / f = (1.5 -1) 1 / 16.5

         1 / f = 0.03030

          f = 33 cm

convex       f = 33 cm

concave     f = -33 cm

Answer:

(a) The work function is 1.86 eV.

(b) The cut off frequency is 450 THz.

(c) The stopping potential is 1.16 V.

Explanation:

incident wavelength = 620 nm

Kinetic energy, K = 0.14 eV

According to the photoelectric equation

E = W + KE

where, W is the work function, KE is the kinetic energy.

(a) Let the work function is W.

[tex]W = E - KE\\W = \frac{h c}{\lambda }- KE\\W =\frac{6.63\times 10^{-34}\times3\times 10^{8}}{620\times 10^{-9}\times 1.6\times 10^{-19}}-0.14\\\\W =1.86 eV[/tex]

(b) Let the cut off frequency is f.

W = h f

[tex]1.86\times 1.6\times 10^{-19} = 6.63\times 10^{-34}\times f\\f = 4.5\times 10^{14} Hz =450 THz[/tex]

(c) Let the stopping potential is V.

[tex]E = W + eV\\\frac{6.63\times 10^{-34}\times 3\times 10^{8}}{420\times 10^{-9}\times 1.6\times 10^{-19}}=1.8 + eV\\\\V = 1.16 V[/tex]

Ship handling is both a science and an art. Science because it requires knowledge of various forces acting on the ship. Art because it requires the skills of an experienced navigator to use these forces in his favour. We may learn the science part from the various ship handling courses.

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Answer:

the ratio Kf : Ki is  1 / 4 or 1 : 4

Explanation:

Given the data in the question;

Since this is a perfectly inelastic collision, momentum is conserved;

[tex]P_{initial[/tex] = [tex]P_{final[/tex]

Now for BLOCK 1

mass = M₁ = M

KE = K[tex]_i[/tex]

[tex]\frac{1}{2}[/tex]mv[tex]_i[/tex]₁² = K[tex]_i[/tex]

we solve for v[tex]_i[/tex]₁

mv[tex]_i[/tex]₁² = 2K[tex]_i[/tex]

v[tex]_i[/tex]₁ = √( 2K[tex]_i[/tex] / m )

for BLOCK 2

mass = M₂ = 3m and since its at rest v[tex]_i[/tex]₂ = 0

Now after the collision; Total mass = m + 3m = 4m

KE = K[tex]_f[/tex]

[tex]\frac{1}{2}[/tex]( 4m )v[tex]_f[/tex]² = K[tex]_f[/tex]

(2m)v[tex]_f[/tex]² = K[tex]_f[/tex]

v[tex]_f[/tex] = √(K[tex]_f[/tex] / 2m)

so since [tex]P_{initial[/tex] = [tex]P_{final[/tex]

[m₁ × v[tex]_i[/tex]₁] + [m₂ × v[tex]_i[/tex]₂] = ( m + 3m ) × v[tex]_f[/tex]

so

[ m₁ × √( 2K[tex]_i[/tex] / m ) ] + [ m₂ × 0 ] = ( m + 3m ) × [ √(K[tex]_f[/tex] / 2m) ]

[ m × √( 2K[tex]_i[/tex] / m ) ] = 4m × [ √(K[tex]_f[/tex] / 2m) ]

square both side

m² ×  2K[tex]_i[/tex] / m  = (4m)² × K[tex]_f[/tex] / 2m

m² ×  2K[tex]_i[/tex] / m  = 16m² × K[tex]_f[/tex] / 2m

m × 2K[tex]_i[/tex]  = 8m × K[tex]_f[/tex]

2K[tex]_i[/tex]  =  8K[tex]_f[/tex]

K[tex]_f[/tex] = 2K[tex]_i[/tex] / 8

K[tex]_f[/tex] / K[tex]_i[/tex] = 2 / 8

K[tex]_f[/tex] / K[tex]_i[/tex] = 1 / 4

Therefore,  the ratio Kf : Ki is  1 / 4 or 1 : 4

The ratio of the final kinetic energy to initial kinetic energy of the blocks is determined as 1:4.

The speed of the two blocks after collision is determined by applying the principle of conservation of linear momentum as follows;

m1u1 + m2u2 = v(m1 + m2)

mu1 + m2(0) = v(m + 3m)

mu1 = v(4m)

u1 = 4v

[tex]\frac{K.E_f}{K.E_i} = \frac{0.5(4m)v_f^2}{0.5(m)u_1^2} \\\\\frac{K.E_f}{K.E_i} = \frac{4(v_f)^2}{u_1^2} \\\\\frac{K.E_f}{K.E_i} = \frac{4v_f^2}{(4v_f)^2} = \frac{4v_f^2}{16v_f^2} = \frac{1}{4} = 1:4[/tex]

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Answer:

Explanation:

Geostationary satellites orbit around the Earth at the same rate as the Earth rotates so that the satellites are over the same spot on Earth all the time.

They are called geostationary due to their movement.

Geostationary satellites are a key tool for scientists to monitor and observe the Earth's atmosphere.  

Answer:

100N in the opposite direction

Explanation:

as the block is not moving, we can apply the formula f=ma where the total force is equal to the mass times accelaration, since the block is not moving, the net force is zero meaning that the other force is completely cancelling out the force of 100N, or to put it in a maths equation, 100-force=0 as the block is stationary. we can therefore assume that the force cancelling the 100N out is equal to it and therefore 100N in the opposite direction

Answer:

1.20Nm

Explanation:

Given data

Force= 53.5N

Perpendicular distance= 2.25cm= 2.25/100= 0.0225m

The expression for the torque is given as

Torque= Force* Perpendicular distance

Torque= 53.5*0.0225

Torque= 1.20Nm

Hence the toque produced is  1.20Nm